"Curve From Mesh/Text" not working on wireframe of cube
Conversion to wireframe does this in essence, for every face on a Mesh.



The wireframe conversion transforms each face into thin faces interior to  the perimeter of the face, this function has parameters that you can change to adjust the width of those faces, but by default it is rather thin.


  As a side note: The Curve from Mesh/Text conversion tool operates best on Meshes if you remove the faces first. (X, remove only faces). If the mesh doesn't have any Faces there is no need to convert to wire-frame (or remove doubles later on).


You can set the thickness of the wireframe to 0.000, and then you'll see little dots on the edges, because it still creates faces but they are so thin they will fall below the 'remove doubles' limit:



Removing doubles would look like this:



At this point you can convert to Curve from Mesh/Text. But I doubt that is actually what you want.



If you follow the link in the first comment on your Question you will be able to render results like this:



Conversion to wire-frame isn't the way to go about rendering with face occlusion.